"Philosophers say a great deal about what is absolutely necessary for science, and it is always, so far as one can see, rather naive, and probably wrong."
Richard Feynman

This topic is really in two parts: First, the education of physics undergraduate and graduate students; second, the study of physics education, usually called Physics Education Research (PER). For the first group (undergrads and grads), I offer discussions on what to expect, typical coursework, and discussion of various, representative problems. For detailed problems (with solutions) see each individual topics under physics topics. For the second group, I offer discussions of the Inquiry Method and the Modeling Method, the two pedagogical methods I have studied. See links at left for organizations that study PER. Discussions are below, so please browse about and be sure to visit the Question Board if you'd like to ask a question or post a comment!

Undergraduate Info

Modeling Method

Inquiry Method

Undergraduate study in physics is typically a whirlwind tour of many topics, few of which are studied in tremendous detail. However, there are always exceptions in each program, so I'll do my best to cover the most general problems, reflective of the largest common denominator.

As a physics undergraduate, you can expect the freshman physics course to be perhaps the most difficult. It's not that the topics are covered in depth, nor do they require an extensive amount of mathematics, but the typical freshman course covers a million and one topics very quickly!

A standard approach is to then study the topics you covered in freshman physics in more detail over the next few years. You'll concentrate on classical mechanics (using differential equations), electro and magnetostatics (using vector calculus), thermodynamics (using statistical methods), and quantum mechanics (the wave mechanics, but perhaps also some matrix mechanics). Of course, you'll also study other topics like nuclear physics or optics or electronics or acoustical physics, but the four areas I've mentioned tend to form the core of your work.

With that in mind, it is from those four areas that I've selected some representative problems to present here.

...more to come...
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In its essence, the Modeling Method does two very important things for students. First, it gives them a real context in which to apply their understanding of things (more on this in a bit). Second, and more importantly (in my opinion), it gives students a sense that they are capable at finding things out.

Okay, that's all philosophically interesting, but what are the nuts and bolts of the Modeling Method? How would you implement it in a classroom?

Nuts and Bolts of Modeling Method

I'm sure that each person who practices the Modeling Method does it in a slightly (or even not-so-slightly) different format. For the authoritative version, you can use the link to Arizona State under Resources, above. I like my "boiled down" approach because, frankly, I'm not a physics education researcher, I'm just a physics educator. Therefore, I don't consider it my job necessarily to add to the physics education research literature but rather to apply what they come up with in a manner that works in my classrooms (I've taught mostly at the high school level). And that's what I present here.

1. Observe. Observation means the students are shown a demonstration of the equipment that they are to use. In this demonstration, I not only show how the equipment works, but also what the phenomenon looks like. For example, when investigating pendula, the students observe a pendulum swinging back and forth.

2. Categorize. After a bit of observation, the students must determine the variables for the system, for example the length of the pendulum string, the mass of the pendulum bob, etc. Then, they categorize these variables into Causes and Effects. For example, students may consider the length of the string to be a Cause, since it is set by the experimenter, while they may consider the time for one swing (the period) to be an Effect, since other factors (i.e., Causes) may influence it. Once they have a nice list of Causes and Effects (aka, Independent and Dependent variables, respectively), they then pair some of them up. For example, one group may feel that the bob mass causes changes in the period, while another may feel that it's the string length that causes changes in the period.

3. Experiment. Now that various groups of students have their own categorizations, it's time to let them loose. They get a copy of the equipment and are told to gather data regarding how their variables are related. It's okay to step in and help ensure data integrity at this point! What I mean is, some students don't understand why it is necessary to only vary one variable at a time over several trials... But as the term goes on, all the groups catch on eventually.

4. Build Models. Once the groups have their data, they must build graphical and mathmatical models to represent the relationships between their variables. Usually, the graphical models are not linear, so they need to linearize the graphs (which they have specific instructions for accomplishing, and I'm more involved in this phase to help anyone struggling with data analysis). Once the graphs are put together and linearized, they can analyze the slope and intercept information, taking into account which variables are on which axis, and come up with an algebraic statement relating their variables. This is really a key step because it is conceptually difficult for most students to see graphical information as algebra statements, and vice versa. It helps that they've seen the physical behavior, but it's still a difficult step.

5. Assess Models. This is a fun step, because it involves a lot of interaction among the students. They are responsible for presenting their models to the rest of the class for peer review. Typically, this is done on portable white boards. Each group has one, and prepares their presentation on it. After each presentation, other groups ask for justification of data or analysis, they ask about whether the units on the slope make physical sense, they ask for connections between the observed behavior and the final models, etc. In other words, they engage in science.

A key thing here is that it's okay to be wrong! If it turns out that a group's model is incorrect, they collaborate with other groups who looked at those same variables. If each group used unique sets of variables, then they figure out what they think went wrong and fix it. Really, it's no different than if they were actual researchers! And that is what comes across so powerfully to the students; they feel like actual scientists, and therefore, they feel capable of doing science, of thinking on their own, and of being responsible for their educations.

Implementing

The way that I have implemented the Modeling Method is to simplify what I expect to teach in any particular term or year. I remember my first year of teaching... My list of Yearly Learning Objectives would have rivaled any course! Luckily my science department chair told me to scale back... And I did, and it was the right move.

I'd rather have my students understand a few concepts very well than introduce them to many concepts that they only just barely grasp. Solid conceptual understanding takes time! The Modeling Method helps me to not rush... As Joe Reddish (a physics education guru) says, "It's not about covering a lot of material, it's about uncovering students' real understanding."

With that in mind, I trim my list of topics to be those topics that can work in a Modeling situation. If a certain topic is not a good candidate for doing it as a Model (using the five steps, above), then I tend to not include that topic in the Yearly Learning Objectives. Granted, there are things we discuss and learn about that are not done in a Modeling mode, but the weight of my teaching time is spent using the Modeling Method.

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The Inquiry Method has two main flavors, directed and open inquiry. Directed inquiry is most of what folks in PER mean when they say "inquiry," and it is, at its roots, a series of questions designed to lead the student to a particular understanding of a concept. Socratic questions are the heart and soul of any type of inquiry, and form the foundation for illuminating and eliminating misconceptions.

Again, theoretically interesting, but how does this work in practice? How can you implement this in the classroom?

Despite the many research hours spent in the last couple of decades, there is really nothing terribly complex about implementing the Inquiry Method. It comes down to a single tenent: Answer questions with questions. When a student asks, "Hey, teach! Should this graph be curved?" you avoid the standard response of, "Well, yes, we're dealing with constant accleration and that is a distance-time graph, so, yes, it should be curved" and instead, innocently ask, "Well, should it?"

Okay, yes, this can frustrate some students. And while the goal is not to over frustrate anyone, a little frustration is a very, very good thing for quality learning. Think of it like exercising, if you want. Doing one rep with a light weight, once a week, will net you no increase in fitness (giving the answer to the student). It's too easy, and your body never has to adjust. But, do varying reps with varying weights, several times a week (different muscle group each time), and your body will adjust to the increased work-load, i.e., you will get more fit (engaging the student in a socratic dialogue about the concept). Likewise, doing too many reps with too much weight, too many times each week, will result in injury (never providing any guidance, or using questions as a method to demean students).

In PER, like I said, the emphasis is on directed inquiry. So, much time and effort is spent discovering where students have the largest conceptual misunderstandings. Curricular materials get designed around exposing and resolving these misconceptions, and the results are put together in work-book format. These work-books make very useful materials to use in a classroom, whether as a supplement or as a primary motivator of the learning. But be careful, since the level of expertise you may expect students to gain in a topic may be different than the researchers who wrote the work-book!

Typically, inquiry-based materials are exhaustively complete, and it's best to pick and choose the topics you want to do in an inquiry style.

Personally (for what it's worth), I prefer the Modeling approach to the Inquiry approach as a working classroom strategy, mostly for the hands-on nature of modeling. But, I certainly value the inquiry philosophy very much, and while using the Modeling approach, I engage students in an Inquiry mode, using Socratic questions as much as possible. I also simply give them answers sometimes, if I feel they've wrestled long enough with a concept and are simply stuck. As with most things, it is best to mix and match rather than stick to one method religiously over another, and it is never effective teaching to not adjust your teaching strategies when faced with the needs of individual students.

The question is, do you want to be effective, or do you want to be right? I want to be effective, so I try to pick and choose from the best available strategies, rather than use one exclusively, and remember the fundamental rule of human relationships: when you trust and respect someone, you earn their trust and respect. It must be no different for the relationship between student and teacher.

... more to come ...

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